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Family of Sets

Date: September 29 2022

Summary: A simple overview on what a family of sets actually is

Keywords: ##summary #set #family #subset #archive

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Table of Contents

    1. Reading Motivation
    2. Family of Sets
  1. How To Cite
  2. References:
  3. Discussion:

Reading Motivation

I am having trouble reading some set theoretic notation. Hoping by gaining better familiarity with family of sets, I can understand notation better.

Family of Sets

In brief, a family of sets could be the following:

Definition 1: A family of sets, FF, could be a set of subsets over a set XX. An example of this would be the following scenario:

Let X=1,2,3,4X = {1, 2, 3, 4}

F={{},{1,2},{3,4}} F = \{\{\emptyset\}, \{1, 2 \},\{3, 4\}\} F F

is non-exhaustive as there could be more subsets derived from XX.

Definition 2: A family of sets, FF, could be a set of sets where each set is independent from the others. An example of this would be the following scenario:

Let A={1,2,3}A = \{1, 2, 3\}, B={4,5,6}B = \{4, 5, 6\}, and C={2,4,6}C = \{2, 4, 6\}

F={A,B,C}={{1,2,3},{4,5,6},{2,4,6}} F = \{A, B, C\} = \{\{1, 2, 3\}, \{4, 5, 6\}, \{2, 4, 6\}\}

How To Cite

Zelko, Jacob. Family of Sets. https://jacobzelko.com/09302022033236-family-sets. September 29 2022.

References:

Discussion:

CC BY-SA 4.0 Jacob Zelko. Last modified: July 16, 2023. Website built with Franklin.jl and the Julia programming language.